How do you simplify #(8x+16) / (x^2-1 )*( x+1)/(4x+8)#?

Question

Hazel Anglin · Accepted Answer

The answer is #2/(x-1)#.

#(8x+16)/(x^2-1) * (x+1)/(4x+8)# Factor out #2# from #(8x+16)#. #(2(4x+8))/(x^2-1) * (x+1)/(4x+8)# Cancel #(4x+8)# in the numerator and denominator. #(2cancel(4x+8))/(x^2-1) * (x+1)/cancel(4x+8)=# #2/(x^2-1) * (x+1)/1# Factor #x^2-1#. #2/((x+1)(x-1)) * (x+1)/1# Cancel #x+1# in the numerator and denominator. #2/(cancel(x+1)(x-1)) * cancel(x+1)/1=# #2/(x-1)#

Genesis Allen · Answer

undefined To simplify the expression (8x+16) / (x^2-1) * (x+1)/(4x+8), we can start by factoring the numerator and denominator.

The numerator (8x+16) can be factored as 8(x+2), and the denominator (x^2-1) can be factored as (x+1)(x-1).

The expression can now be written as 8(x+2) / [(x+1)(x-1)] * (x+1)/(4x+8).

Next, we can simplify further by canceling out common factors. The (x+1) term in the numerator and denominator can be canceled out.

The expression simplifies to 8(x+2) / (x-1) * 1/(4x+8).

Further simplification can be done by canceling out the common factor of 8 in the numerator and denominator.

The final simplified expression is (x+2) / (x-1) * 1/(x+2).

Therefore, the simplified expression is (x-1) / (x+2).